Points \(P\), \(Q\), \(R\) and \(S\) divide the respective sides of rectangle \(ABCD\) in the proportion \(1:2\). If the area of rectangle \(ABCD\) is \(1\), find the area quadrilateral \(PQRS\).
+128475 [ ABCD ] = width * height = 1 = wh
Area of right triangle DRS = area of right triangle PBQ = (1/2) (2/3)w* (1/3) h = ( 1/9)wh
Area of right triangle RCQ = area of triangle SAP = (1/2) ( 1/3) h ( (2/3)w = ( 1/9)wh
So these combined areas = 4 ( 1/9) wh = (4/9) wh = (4/9) (1) =4/9
[ PQRS ] = [ ABCD ] - 4/9 = 1 - 4/9 = 5/9
